솔루션피아

$$ \begin{cases} m_A&=0.270\ut{kg}\\ \vec v_{\text{in}}&=-12.0\j\ut{m/s}\\ \vec v_{\text{out}}&=+3.00\j\ut{m/s}\\ \vec v_B&=0 \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta \vec P_A&=\Delta (m_A\vec v_A)\\ &=m_A\Delta \vec v_A\\ &=m_A (\vec v_{Af}-\vec v_{Ai})\\ &=m_A (\vec v_{\text{out}}-\vec v_{\text{in}})\\ &=\frac{81}{20}\j\ut{kg\cdot m/s}\\ &=4.05\j\ut{kg\cdot m/s}\\ \end{aligned} $$ $..

$$ \begin{cases} m_A&=75\ut{kg}\\ m_B&=50\ut{kg}\\ v_i&=2.3\ut{m/s}\\ v_{Af}&=0 \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} \vec P_i&=\vec P_{Af}+\vec P_{Bf}\\ (m_A+m_B)v_i&=m_Av_{Af}+m_Bv_{Bf}\\ &=m_Bv_{Bf}\\ \end{aligned} $$ $$ v_{Bf}=\frac{m_A+m_B}{m_B}v_i $$ $$ \begin{aligned} \Delta v_B&=v_{Bf}-v_{Bi}\\ &=\frac{m_A+m_B}{m_B}v_i-v_{i}\\ &=\frac{m_A}{m_B}v_i\\ &=+\frac{69}{2..

$$ \put \begin{cases} A:m_1\\ B:m_2\\ C:m_3\\ \end{cases} $$ $$ \put \begin{cases} 0:\text{Start}\\ 1:\text{After A,B Crash}\\ 2:\text{After B,C Crash}\\ \end{cases} $$ $$ \begin{cases} m_A&=4m\\ m_B&=0.500m_A=2m\\ m_C&=0.500m_B=m \end{cases} $$ $$ \begin{cases} v_{A0}&=2.00\ut{m/s}\\ v_{B0}&=0\\ v_{C0}&=0\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \text{Elastic Collision}\Harr\vec v_{\text..

$$ \put \begin{cases} A:m_1\\ B:m_2\\ C:m_3\\ \end{cases} $$ $$ \put \begin{cases} 0:\text{Start}\\ 1:\text{After A,B Crash}\\ 2:\text{After B,C Crash}\\ \end{cases} $$ $$ \begin{cases} m_A&=m\\ m_B&=2.00m\\ m_C&=2.00m_B=4.00m \end{cases} $$ $$ \begin{cases} v_{A0}&=2.00\ut{m/s}\\ v_{B0}&=0\\ v_{C0}&=0\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \text{Elastic Collision}\Harr\vec v_{\text{in}..

$$ \begin{cases} F&=750\ut{N}\\ k&=2.5\times10^5\ut{N/m}\\ \end{cases} $$ $$\ab{a}$$ $$F=kx,$$ $$ \begin{aligned} x&=\frac{F}{k}\\ &=3.0\times10^{-3}\ut{m}\\ &=3.0\ut{mm}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} W&=\frac{1}{2}kx^2\\ &=\frac{1}{2}k\(\frac{F}{k}\)^2\\ &=\frac{F^2}{2k}\\ &=\frac{9}{8}\ut{J}\\ &=1.125\ut{J}\\ &\approx 1.1\ut{J} \end{aligned} $$ $$\ab{c}$$ $$F=kx,$$ $$\ab{d}$..

$$ \begin{cases} v_{A1}&=2.00\ut{m/s}\\ v_{B1}&=2.60\ut{m/s}\\ v_{A2}&=6.00\ut{m/s}\\ \end{cases} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \(\frac{1}{2}m{v}^2\)&=-\Delta (mgy)\\ \Delta \({v}^2\)&=2g(-\Delta y)\\ {v_f}^2-{v_i}^2&=2g(-\Delta y)\\ &=\Cons\\ \end{aligned} $$ $${v_{B2}}^2-{v_{A2}}^2={v_{B1}}^2-{v_{A1}}^2$$ $$ \begin{aligned} v_{B2}&=\sqrt{{v_{A2..

$$ \begin{cases} L&=230\ut{cm}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} 0:\text{Start}\\ 1:\text{Lowest Point}\\ 2:\text{Over P Highest Point} \end{cases} $$ $$ \begin{cases} y_0&=L\\ y_1&=0\\ y_2&=2r\\ \end{cases} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$ \begin{aligned} \Delta \KE&=-\Delta \GE\\ \Delta \(\frac{1}{2}m{v}^2\)&=-\Delta (mgy)\\ \Delta \({v}^2\)&=2..

$$ \begin{cases} m&=3.6\ut{kg}\\ y&=3.8\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \GE&=mgy\\ &=\frac{342g}{25}\\ &=134.154972\ut{J}\\ &\approx 1.3\times10^2\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$\Sigma \Delta E=0,$$ $$ \begin{aligned} \KE&=\GE\\ &=134..

$$ \begin{cases} v_i&=7.0\ut{m/s}\\ h&=2.0\ut{m}\\ \mu&=0.50\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE+\Delta \TE=0$$ $$ \begin{aligned} \Delta \TE&=-\Delta \KE-\Delta \GE\\ fd&=-\Delta\(\frac{1}{2}mv^2\)-\Delta (mgy)\\ \mu m g d&=-\..

$$ \begin{cases} m&=5.0\ut{kg}\\ k&=425\ut{N/m}\\ x&=6.0\ut{cm}=0.06\ut{m}\\ \mu&=0.25\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \LE : \text{Elastic Potential Energy}\\ \TE : \text{Thermal Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} W_s&=-\Delta \LE\\ &=\LE_i-\LE_f\\ &=-\LE_f\\ &=-\frac{1}{2}kx^2\\ &=-\frac{153}{200}\ut{J}\\ &=-0.765\ut{..